Uncorrelated Model Research Articles

Assessing the content typicality and construct of Persian language proficiency test (PLPT) for non-Persian speakers: a corpus-informed study

Drawing on a growing body of research on the interface between corpus linguistics and second/foreign language testing and assessment, we adopted Peykare, a large-scale, annotated, Persian written language resource to evaluate the content (i.e., coverage and typicality) and construct validity of a Persian language proficiency test developed for certification of proficiency in Persian as a foreign language (PFL) of non-native speakers. Designed at the Research Center for Intelligent Signal Processing (RCISP), Peykare contains 35,058 text files over five linguistic varieties and 24 different registers of contemporary Persian. This study addresses how corpora, as rich database resources, can practically be applied to test validation purposes and insightfully inform the test life cycle. The results of content validity phase revealed evidence supporting content representativeness, relevance, and typicality of the test. The linkage between the corpus-extracted criterial features or parameters and those covered by the test was not, however, strongly evidenced by items measuring ezafeh constructions, homographs/homophones, PRO (proposition), and POST (postposition). The analysis of content typicality indicated chunks that did not closely conform to the corpus typical output. The construct validity phase, assessing the test hypothesized factor structure (i.e., hierarchical, unitary, correlated, and uncorrelated models) in two randomly split samples of PFL learners from Asian and European countries (N=121), showed that the correlated model fit the data best in both samples. The results supported the presence of distinctive factors of receptive skills, providing empirical evidence for score interpretations of the corpus-based test.

Assessment of the impact of noise magnitude and bandwidth variations on a probabilistic inversion of reflection seismic data

AbstractAccounting for an accurate noise model is essential when dealing with real data, which are noisy due to the effect of environmental noise, failures and limitations in data acquisition and processing. Quantifying the noise model is a challenge for practitioners in formulating an inverse problem, and usually, a simple Gaussian noise model is assumed as a white noise model. Here we propose a pragmatic approach to use an estimated seismic wavelet to capture the correlated noise model (coloured noise) for the processed reflection seismic data. We assess the proposed method through a direct inversion of post‐stack seismic data associated with a carbonate reservoir of an oil field in southwest Iran to porosity, using a probabilistic sampling‐based inversion algorithm. In the probabilistic formulation of the inverse problem, we assume eight different noise models with varying bandwidth and magnitude and investigate the corresponding posterior statistics. The results indicate that if the correlated nature of the noise samples is ignored in the noise covariance matrix, some unrealistic features are generated in porosity realizations. In addition, if the noise magnitude is underestimated, the inversion algorithm overfits the data and generates a biased model with low uncertainty. Furthermore, by considering an imperfect bandwidth for the noise model, the error is propagated to the posterior realizations. Assuming the correlated noise in a probabilistic inversion resolves these issues significantly. Therefore, for inverting real seismic data where the estimation of the magnitude and correlations of the noise is not straightforward, the wavelet, which is estimated from the real seismic data, provides a good proxy for describing the correlation of the noise samples or equivalently the bandwidth of the noise model. In addition, it might be better to overestimate the noise magnitude than to underestimate it. This is true especially for an uncorrelated noise model and to a lesser degree also for the correlated noise model.

No phylogenomic support for a Cenozoic origin of the "living fossil" Isoetes.

The isoetalean lineage has a rich fossil record that extends to the Devonian but the age of the living clade is unclear. Recent results indicate that it is young, from the Cenozoic, whereas earlier work based on less data from a denser taxon sample yielded Mesozoic median ages. We investigated node ages in Isoetes using two genomic datasets (plastome and nuclear ribosomal cistron) analyzed using three different clock models implemented in MrBayes (ILN, WN and TK02 models) and a conservative approach to calibration. While topological results are consistently resolved in Isoetes estimated crown group ages range from the latest Paleozoic (mid-Permian) to the Mesozoic depending on datatype and clock model. The oldest estimates were retrieved using the autocorrelated TK02 clock model. An (early) Cenozoic age was only obtained under one specific condition (plastome data analyzed with the uncorrelated ILN clock model). That same plastome dataset also yielded the oldest (mid-Permian) age estimate when analyzed with the autocorrelated TK02 clock model. Adding the highly divergent recently established sister species Isoetes wormaldii to the dataset approximately doubled the average median node depth to the Isoetes crown group. There is no consistent support for a Cenozoic origin of the living clade Isoetes. We obtained seemingly well-founded, yet strongly deviating, results depending on datatype and clock model. The single most important future improvement is probably to add calibration points, which requires an improved understanding of the isoetalean fossil record or alternative bases for calibration. This article is protected by copyright. All rights reserved.

Phylogeography of hepatitis B virus: The role of Portugal in the early dissemination of HBV worldwide.

In Portugal, the genetic diversity, origin of HBV and the Portuguese role in the dissemination of HBV worldwide were never investigated. In this work, we studied the epidemic history and transmission dynamics of HBV genotypes that are endemic in Portugal. HBV pol gene was sequenced from 130 patients followed in Lisbon. HBV genotype A was the most prevalent (n = 54, 41.5%), followed by D (n = 44, 33.8%), and E (n = 32, 24.6%). Spatio-temporal evolutionary dynamics was reconstructed in BEAST using a Bayesian Markov Chain Monte Carlo method, with a GTR nucleotide substitution model, an uncorrelated lognormal relaxed molecular clock model, a Bayesian skyline plot, and a continuous diffusion model. HBV subgenotype D4 was the first to be introduced in Portugal around 1857 (HPD 95% 1699-1931) followed by D3 and A2 a few decades later. HBV genotype E and subgenotype A1 were introduced in Portugal later, almost simultaneously. Our results indicate a very important role of Portugal in the exportation of subgenotypes D4 and A2 to Brazil and Cape Verde, respectively, in the beginning of the XX century. This work clarifies the epidemiological history of HBV in Portugal and provides new insights in the early and global epidemic history of this virus.

Cross-section asymptotic for random-effects panel data models with autoregressive errors

A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior.

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative data sets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student $t$ process regression. We apply Student $t$ process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via colouring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics and classic machine learning clustering algorithms.

Underwater Navigation of AUVs Using Uncorrelated Measurement Error Model of USBL

<i>This article presents a modeling method for the uncorrelated measurement error of the ultra-short baseline (USBL) acoustic positioning system for aiding navigation of underwater vehicles. The Mahalanobis distance (MD) and principal component analysis are applied to decorrelate the errors of USBL measurements, which are correlated in the x- and y-directions and vary according to the relative direction and distance between a reference station and the underwater vehicles. The proposed method can decouple the radial-direction error and angular direction error from each USBL measurement, where the former and latter are independent and dependent, respectively, of the distance between the reference station and the vehicle. With the decorrelation of the USBL errors along the trajectory of the vehicles in every time step, the proposed method can reduce the threshold of the outlier decision level. To demonstrate the effectiveness of the proposed method, simulation studies were performed with motion data obtained from a field experiment involving an autonomous underwater vehicle and USBL signals generated numerically by matching the specifications of a specific USBL with the data of a global positioning system. The simulations indicated that the navigation system is more robust in rejecting outliers of the USBL measurements than conventional ones. In addition, it was shown that the erroneous estimation of the navigation system after a long USBL blackout can converge to the true states using the MD of the USBL measurements. The navigation systems using the uncorrelated error model of the USBL, therefore, can effectively eliminate USBL outliers without loss of uncontaminated signals.</i>

Real-space numerical renormalization group computation of transport properties in side-coupled geometry

A real-space formulation of the numerical renormalization group (NRG) procedure is introduced. The real-space construction, dubbed eNRG, is more straightforward than the NRG discretization, and allows a faithful description of the coupling between quantum dots and conduction states even if the design of the couplings is intricate. General features of the two procedures are discussed comparatively. A more specific comparison is then developed, based on computations of the zero-bias transport properties for an Anderson-model description of a quantum wire side-coupled to a single quantum dot. An eNRG computation is shown to reproduce accurately the temperature-dependent electrical conductance for the uncorrelated model in the continuum limit, while significant deviations mark the corresponding NRG computation for thermal energies comparable to the conduction bandwidth. A combination of analytical and numerical results for the transport properties of the correlated model then provides a more exacting check on the accuracy of the eNRG procedure. A recent NRG analysis mapping the transport properties of a single-electron transistor onto universal functions of the temperature scaled by the Kondo temperature is extended to the side-coupled device, on the basis of eNRG reasoning. Numerical results for the electrical conductance, thermopower, and thermal conductance in side-coupled geometry are then shown to agree very well with the mappings. The numerical results are also checked against the thermal dependence of the thermopower measured by K\"ohler et al. [Phys. Rev. B 77, 104412 (2008)] in ${\mathrm{Lu}}_{0.9}^{\phantom{\ifmmode\dagger\else\textdagger\fi{}}}{\mathrm{Yb}}_{0.1}^{\phantom{\ifmmode\dagger\else\textdagger\fi{}}}{\mathrm{Rh}}_{2}^{\phantom{\ifmmode\dagger\else\textdagger\fi{}}}{\mathrm{Si}}_{2}^{\phantom{\ifmmode\dagger\else\textdagger\fi{}}}$, and the remarkably accurate, recent conductance measurements by Xu et al. [Chin. Phys. Lett. 38, 087101 (2021)].

Entropy and freezing in Gaussian models

A new definition of the freezing phenomenon is given in relation with the behavior of the entropy of Gibbs measures at low temperatures. In particular, for uncorrelated and log-correlated Gaussian models, we show that freezing arises when the entropy of the corresponding Gibbs measures vanishes.

Model-Based and Data-Driven Approaches for Downlink Massive MIMO Channel Estimation

We study downlink channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in time-division duplex. The users must know their effective channel gains to decode their received downlink data. Previous works have used the mean value as the estimate, motivated by channel hardening. However, this is associated with a performance loss in non-isotropic scattering environments. We propose two novel estimation methods that can be applied without downlink pilots. The first method is model-based and asymptotic arguments are utilized to identify a connection between the effective channel gain and the average received power during a coherence interval. The second method is data-driven and trains a neural network to identify a mapping between the available information and the effective channel gain. Both methods can be utilized for any channel distribution and precoding. For the model-aided method, we derive all expressions in closed form for the case when maximum ratio or zero-forcing precoding is used. We compare the proposed methods with the state-of-the-art using the normalized mean-squared error and spectral efficiency (SE). The results suggest that the two proposed methods provide better SE than the state-of-the-art when there is a low level of channel hardening, while the performance difference is relatively small with the uncorrelated channel model.

The past, present, and future of the Siberian Grouse (Falcipennis falcipennis) under glacial oscillations and global warming

Global climate change has a significant effect on species, as environment conditions change, causing many species' distributions to shift. During the last three million years, the earth has experienced glacial oscillations, forcing some species to survive in ice-free refugia during glacial periods and then disperse postglacially. In this study, by assessing the potential distribution of Siberian Grouse (Falcipennis falcipennis), we used Global Circular Models and Representative Concentration Pathways to model their pattern of range changes during glacial oscillations and the potential impact of present global warming. We used 158 location records of Siberian Grouse to generate a full climate model using 19 bioclimate variables in MaxEnt. We discarded variables with a correlation coefficient larger than 0.8 and relatively lower modeling contributions between each pair of correlated variables. Using the remaining variables, we created a normally uncorrelated simple climate model to predict the possible distribution of Siberian Grouse from the most recent Ice Age to present and to 2070. Then we added geographical data and the human interference index to construct a multiple factor full model to evaluate which were important in explaining the distribution of Siberian Grouse. The Total Suitability Zone (P ​≥ ​0.33) of Siberian Grouse is about 243,000 ​km2 and the Maximum Suitability Zone (P ​≥ ​0.66) is 36,000 ​km2 and is confined to the Russian Far East. Potential habitat modeling suggested that annual precipitation, annual mean temperature, and the distance from lakes are the most explanatory variables for the current distribution of Siberian Grouse. The distribution center moved to the southeast during the Last Glacial Maximum and spread back to the northwest after the ice melted and temperatures rose. The total area range of Siberian Grouse experienced a dramatic loss during the Last Glacial Maximum. Global warming is presently forcing the Siberian Grouse to migrate northward with a contraction of its range. There is an urgent need to protect its habitat, because little of its Maximum Sustainable Zone is protected, although there are some large reserves in that area.

Regulated Emergence of the African swine fever virus: B646L (p72) Gene Based Bayesian Coalescent Analysis

African swine fever virus (ASFV) belongs to the genus of virus of the Asfaviridae family. ASFV infection causes hemorrhage and high death rate hence increased loss to the swine community. It is a complex infectious disease of swine, which constitutes devastating impacts on animal health and the economy of the pig farmers. It has been confirmed that virus infections has been spreading in swine population for many years. In this study, the evolutionary epidemiology analysis of ASF virus from the geographical regions Africa, Europe, and Asia, respectively were retrieved from GenBank for the analysis. The nucleotide gene sequences of the viral protein p72 encoded by B646L gene published during 1960-2020 was taken in to study. The Bayesian skyline model with uncorrelated randomized clock model was employed to reconstruct the evolutionary history of the virus, to identify virus population demographics. Results of the analysis suggested that ASFV exhibited a high evolutionary rate, as the divergence caused reduction in the population in the recent years. The B646L gene of ASFV had an evolutionary rate of 4.13 X 10-6 substitution/site/year and the tMRCA as 3.15 x 105 with 95 percent HPD range in years (2.4 x 104 to 1.23 x 106) was obtained. In conclusion, the evolutionary study of ASFV with p72 protein from the ASFV of the B646L genes indicated that they evolved at a faster rate and plays a major role in the evolutionary process. Further, this study may help in designing or developing vaccines to control the spread of the disease.

Multiparameter viscoelastic full-waveform inversion of shallow-seismic surface waves with a pre-conditioned truncated Newton method

SUMMARY 2-D full-waveform inversion (FWI) of shallow-seismic Rayleigh waves has become a powerful method for reconstructing viscoelastic multiparameter models of shallow subsurface with high resolution. The multiparameter reconstruction in FWI is challenging due to the potential presence of cross-talk between different parameters and the unbalanced sensitivity of Rayleigh-wave data with respect to different parameter classes. Accounting for the inverse Hessian using truncated Newton methods based on second-order adjoint methods provides an effective tool to mitigate cross-talk caused by the coupling between different parameters. In this study, we apply a pre-conditioned truncated Newton (PTN) method to shallow-seismic FWI to simultaneously invert for multiparameter near-surface models (P- and S-wave velocities, attenuation of P and S waves, and density). We first investigate scattered wavefields caused by these parameters to evaluate the coupling between them. Then we investigate the performance of the PTN method on shallow-seismic FWI of Rayleigh wave for reconstructing all five parameters simultaneously. The application to spatially correlated and uncorrelated models demonstrates that the PTN method helps to mitigate the cross-talk and improves the resolution of the multiparameter reconstructions, especially for the weak parameters with small sensitivity such as attenuation and density parameters. The attenuation of Pwaves cannot be inverted reliably due to its negligible sensitivity on the Rayleigh wave. The comparison with the classical pre-conditioned conjugate gradient method highlights the improved performance of the PTN method and thus the benefit of accounting for the information included in the Hessian.

Investigating correlations between illness and defensive behaviour approach: A case of twin cities of Pakistan

Municipal solid waste (MSW) management has emerged as a major problem for modern societies in recent decades. An optimal waste management system is essential to prevent the pollution burden and associated health related issues. This study carries out an empirical evaluation of the illness caused by inadequate solid waste management in the metropolitan of Rawalpindi-Islamabad. The model is based on utility-maximizing consumer behavior and predicted probability of disease in the household is estimated by employing “seemingly uncorrelated bivariate probit model”. Primary data obtained through multistage random sampling that comprises of 849 respondents. The findings show that irregular waste disposal sites in the vicinity of residences cause illness. The key findings indicate that distance from dumpsites and use of contaminated water adversely affect the health outcomes. Furthermore, the results show that respondents were unable to engage in defensive activities due to a lack of awareness. Oft-times, the waste is dumped in illegal sites that is burnt thus causing excessive air and ground water pollution. The results shed light on the respondents' understanding of the negative consequences of excessive waste disposal and study suggests measures that motivate households to engage in defensive activities through effective campaigns and capacity building programmes that ensure sustainable solid waste management.

Western Tethys origin, tropical Asia and tropical America disjunction in Berchemia and reinstatement of Phyllogeiton (Rhamneae, Rhamnaceae)

AbstractDespite the well‐known biogeographic pattern in the Northern Hemisphere of disjunct distributions in plants between eastern Asia and North America, many details regarding the evolution of the disjunction between lineages of tropical Asia and tropical America remain poorly understood. Berchemia (Rhamnaceae), comprising ca. 32 species, is distributed predominantly in tropical regions of east to southeast Asia and North America. However, the phylogeny and biogeography of this genus are still not clear. Furthermore, fossils of the genus have been found in Europe, making it an ideal group to understand the biogeographical story of tropical disjunction in the Northern Hemisphere. With two nuclear (ETS, ITS) and three plastid (petA‐psbJ, psbA‐trnH, trnL‐F) DNA regions, we first reconstructed the phylogeny of Berchemia with Bayesian inference and maximum likelihood approaches. Our results indicated that Berchemia, excluding the African species B. discolor and B. zeyheri, which were placed into the reinstated Phyllogeiton, was well‐supported as monophyletic. Divergence times and ancestral areas were inferred using a Bayesian uncorrelated lognormal relaxed molecular clock model and Bayesian binary MCMC method, respectively. The core Berchemia likely originated in the Western Tethys during the middle Eocene, then formed the tropical Asia and tropical America disjunction during the Oligocene and further diversified in Asia from the early Miocene on. The formation and diversification of the core Berchemia likely resulted from a mixture of geologic events, such as the close of the Tethys Ocean, disappearance of the North Atlantic Land Bridges, uplift of the Qinghai‐Tibetan Plateau, and climatic events, such as the establishment and enhancement of Asian monsoons.

Optimizing a new de-clustering approach for relatively small samples of wind speed with an application to offshore design conditions

The effect of extreme wind speeds in applications for design is of great interest in a variety of fields such as meteorology and coastal engineering. In these fields a common problem is the scarcity of long datasets. To overcome this limitation, a common approach is to utilize the entire available dataset using the Peak-Over-Threshold (POT) approach. In small samples there may be a limited number of extremes and so re-sampling is often beneficial. However, the re-samples are often affected by dependency and the independence limitations are usually disregarded. To alleviate this effect, the DeCA Uncorrelated (DeCAUn) model is proposed taking into account the correlation effect when re-sampling. This model provides an improvement to the current physical De-Clustering Algorithm (DeCA), by re-sampling the samples of DeCA irregularly in time. The methodology proposed in this assessment is illustrated using wind speed data from a high resolution database over the North Sea, the Atlantic Ocean and the Mediterranean Sea. From this evaluation, the DeCAUn model is proposed as an alternative re-sampling strategy for observations irregularly spaced in time.

Phased Arrays for Radio Astronomy, Remote Sensing, and Satellite Communications [Book Review

While phased array antenna technology has been discussed since the early 20th century, it could not be more relevant to the present time, in view of modern complex communication protocols, comprehensive global satellite-navigation systems and detailed remote sensing for environment applications. The publication of this book is, therefore, timely. The authors have produced a comprehensive monograph encompassing antenna theory, (noisy) network theory, and computational electromagnetics (CEM), with a strong focus on the radio astronomy application, which is challenged by low signal-to-noise conditions. Therefore, the objectives of the book are twofold, that is, to 1) clearly define the figure of merit and design aspects of the two types of array antennas in radio astronomy based on the IEEE standards and 2) detail the treatment of noise via the stochastic model and procedure to include them within the network theory model. The multidisciplinary nature of the book makes it a valuable resource to a specialized researcher embarking to work on the subject. Readers primarily interested in noisy electromagnetics are introduced to the stochastic model of different types of noise in connection with correlated and uncorrelated noise models. In particular, the extension to noisy microwave networks is discussed in detail with respect to the interface with optimization algorithms, a topic that should attract a wide readership.

A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics’

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753–1765] provide short term asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using Gauss–Hermite quadrature. We further obtain the option price by similarly integrating the constant elasticity of variance (CEV) option prices without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709–737]. For the uncorrelated SABR model, the new option pricing method is accurate and arbitrage-free across all strike prices.

The uncertainty of CRUST1.0

Abstract As crustal structure models based on seismic and other data are frequently used as a-priori information for further geophysical and geological studies and interpretations (e. g., for gravity inversion), it is important to accurately document their qualities. For instance, the uncertainties in published crustal structures deeply affect the accuracies of produced Moho contour maps. The qualities in seismic crustal models arise from several factors such as the survey method, the spatial resolution of the survey (for example the spacing of the shot points and the recording stations), and the analytical techniques utilized to process the data. It is difficult to determine the uncertainties associated with seismic based crustal depth/Moho depth (MD) models, and even more difficult to use such data for estimating the Moho density contrast (MDC) and its accuracy. However, there is another important observable available today, namely global satellite gravitational data, which are fairly homogeneous v. r. t. accuracy and distribution over the planet. For instance, we find by simple error propagation, using the error covariance matrix of the GOCE TIM5 gravitational model, that this model can determine the MD to a global RMS error of 0.8 km with a resolution of about 1° for a known MDC of 200 kg / m 3 \text{kg}/{\text{m}^{3}} . However, the uncertainty in the MDC will further deteriorate the result. We present a new method for estimating the MD and MDC uncertainties of one model by comparing it with another (correlated or uncorrelated) model with known uncertainty. The method is applied in estimating the uncertainty for the CRUST1.0 MD model from four global models (CRUST19, MDN07, GEMMA1.0, KTH15C), yielding mean standard errors varying between 2 and 4.9 km in ocean regions and between 3.2 and 6.0 km on land regions with overall means of 3.8±0.4 and 4.8 ± 0.6 km 4.8\pm 0.6\hspace{0.1667em}\text{km} , respectively. Also, starting from the KTH15C MDC model, the mean standard error of CRUST1.0 MDC was estimated to 47.4 and 48.3 kg / m 3 \text{kg}/{\text{m}^{3}} for ocean and land regions, respectively.

Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: an investigation into propagating uncertainties for independent model parameters

Based on the Monte Carlo approach and conventional error analysis theory, taking the heaviest doubly magic nucleus $$^{208}\hbox {Pb}$$ as an example, we first evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energy in the phenomenological Woods–Saxon mean field. Accepting the Woods–Saxon modeling with uncorrelated model parameters, we found that the standard deviations of single-particle energy obtained through the Monte Carlo simulation and the error propagation rules are in good agreement. It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties. Further, the correlation properties of the single-particle levels within the domain of input parameter uncertainties are statistically analyzed, for example, with the aid of Pearson’s correlation coefficients. It was found that a positive, negative, or unrelated relationship may appear between two selected single-particle levels, which will be extremely helpful for evaluating the theoretical uncertainty related to the single-particle levels (e.g., K isomer) in nuclear structural calculations.